Method and system for damping vibrations in a tool string system

ABSTRACT

The invention provides a control system and method for limiting vibrations in a tool string system, comprising a relatively heavy rotatable device, such as a pump system or a bottom hole assembly, connected to a long rotatable tool string driven by a drive system. The control system comprises feedback of both torque and rotational speed signals to correct the set rotational speed. An objective is to maintain the drive speed over torque ratio equal to the connected tool string impedance. A secondary objective, for lower frequencies, is to approach and maintain a setpoint speed as drive rotation speed. The system may include a rotational speed sensor and a torque sensor, with the latter optionally replaced by a motor torque signal already available from a variable frequency drive (VFD) for an AC motor and the current safeguarding signal for a DC motor.

The present invention relates to a method and to a system for dampingvibrations in a tool string system.

This invention relates generally to mitigation of vibrations in systemshaving a mechanical driving element connected via a rod or tube ofsubstantial length, to a mechanically driven element. The system mayinclude a drilling system or a pump system, for instance for pumpingoil.

As disclosed in U.S. Pat. No. 7,645,124, in general, any driveconnection in a mechanical system exhibits some degree of compliance,i.e. a tendency to yield or bend under load, within the elastic limit ofthe material, or materials, of the components making up the connection.As a result of this compliance, a driving force exerted at one end ofthe connection causes the connection to stretch, bend, and/or twist,depending upon the nature of the connection, in such a manner that thedriving force will be out of phase with a corresponding reaction of adriven element at the opposite end of the connection, due to inertia ofthe driven component which must be overcome in order for the drivingforce to cause a motion of the driven element consistent with the motionof a driving element applying the driving force.

Under certain circumstances, depending upon construction of the system,compliance in the connection will cause an undesirable oscillating orresonant motion to be set up between the driving and driven elements.

Such oscillating behavior is sometimes observed in a system having anengine connected to an engine testing dynamo through a connectionincluding an in-line torque sensor. Such torque sensors typicallyinclude a resilient element operatively joining an input element and anoutput element of the torque sensor. The resilient element allows theinput and output elements to twist slightly, with respect to oneanother, in response to torque being transmitted through the torquesensor. This twisting can be measured and used to determine the torquebeing transmitted by the coupling.

During an increase and/or decrease in torque, however, the resilientelement may cause the system to oscillate as energy is alternatelystored and released by the resilient element, until equilibrium isachieved. Such oscillation can be damaging or otherwise detrimental tooperation of the system and its components. It is desirable, therefore,to provide an apparatus and method for estimating such behavior, and forcontrolling the system in such a manner that the undesirable oscillatoryor resonant behavior is precluded and/or held within acceptable bounds.It is also highly desirable, in some circumstances, to provide for suchcontrol without having sensors located at the driven element, i.e. atthe dynamo in the example given above, in order to remove complexity andcost and to improve reliability of the system.

In some systems, oscillating or resonant behavior takes a form known asstick-slip behavior. Stick-slip behavior refers to an undesiredintermittent form of motion that sometimes occurs between relativelymoving parts where the coefficient of kinetic friction between the partsis less than the coefficient of static friction between the parts.Contacting surfaces of the parts will stick to one another until adriving force, being exerted on one of the parts by a drive element tocause relative movement between the parts, reaches a value high enoughto overcome the static frictional force between the contact surfaces.

Due to the fact that the static coefficient of friction is higher thanthe kinetic coefficient of friction, once the static friction force isovercome by the driving force, the contact surfaces of the parts willtend to move freely and rapidly with respect to one another.

Because there is an inherent springiness (compliance) in the driveelement applying force between the parts, the drive element will tend tostretch or compress, or wind up, as force is applied to the movable partwhile the contact surfaces are being held in contact by the staticfriction force. Once relative motion occurs, this compression, tension,or winding-up of the drive element will cause rapid movement between theparts, to release the energy stored in compression, tension or wind-upof the drive element. Once the stored energy is released, however,through rapid relative movement between the parts, the relative velocitybetween the contact surfaces will drop to the point that the staticfriction force will once again cause the parts to stick to one another,and thereby preclude further relative motion, until sufficientcompression, tension, or wind-up of the drive element once again occurs,to overcome the static frictional force and cause slipping of thecontact surfaces relative to one another.

Stick-slip behavior is sometimes encountered in machinery used inpumping fluids, such as gas, water, or oil, out of the ground. In suchapplications, long shafts, having lengths of hundreds or thousands offeet, may connect a pumping apparatus located far below ground level toa shaft drive mechanism located above ground level. Such long shaftshave considerable inherent springiness, both axially and radially. Thisconsiderable springiness allows a significant amount of energy to bestored in the shaft, if the underground components stick to one another,such that when the torsional force due to wind-up of the shaft becomeshigh enough to cause the underground parts to break free from oneanother, they will slip relative to one another at a very highrotational speed, until the energy stored in the shaft is dissipated.

In one model description, a tool string can be regarded as a torsionalpendulum wherein the top of the tool string rotates with a substantiallyconstant angular velocity, whereas the downhole element performs arotation with varying angular velocity. The varying angular velocity canhave a constant part and a superimposed torsional vibration part. Inextreme cases, the downhole element periodically comes to a completestandstill. Maintaining rotation of the tool string at surface builds uptorque and eventually causes the downhole element to come loose and tosuddenly rotate again, typically leading to a momentary downhole angularvelocity being much higher than the angular velocity at surface. Thishigh angular velocity is typically more than twice the speed (factors of4 to 5 have been observed) of the nominal speed of the drive system atsurface. Thereafter the downhole angular velocity slows down and returnsto zero again where after the process is repeated, causing anoscillating behaviour of the downhole end of the drill string. Thisphenomenon is known as stick-slip.

It is desirable to reduce or prevent these vibrations in order to reduceone or more shock loads to the equipment, avoid reverse rotation, avoidexcessive wear, avoid damage to sensitive well tubulars, and avoidpremature tool failures. High peak speeds occurring during the slipphase can lead to secondary effects like extreme axial and lateralaccelerations and forces. Proper handling of downhole vibrations cansignificantly increase reliability and performance of the equipment.

To suppress the stick-slip phenomenon, control methods and systems havebeen applied in the art to control the speed of the drive system atsurface such that the rotational speed variations of the downhole end ofthe tool string are reduced or prevented.

U.S. Pat. No. 7,645,124-B2 discloses a method to control a downhole pumpsystem exhibiting stick-slip behavior and having unmeasurable states.The method uses a model of the downhole pump system, the model includingreference states of the unmeasurable downhole states. The methodincludes the step of estimating the unmeasurable states and regulatingthe system to minimize differences between the reference states and theestimates. The unmeasurable states include a pump angle estimate and apump speed estimate.

The article “Torque Feedback Used to Cure Slip-Stick Motion” by Halseyet al., 1988, SPE 18049, approaches the problem from yet another angle.A drill string can be regarded as a transmission line for torsionalwaves. A variation of the friction torque at the bit or elsewhere alongthe drill string generates a torsional wave that propagates upwards ordownwards along the drill string and is partially reflected at geometricdiscontinuities. When the transmitted wave reaches the drive system, itis partially reflected back into the drill string. For a drive systemwith a high inertia and/or a stiff speed controller the reflection isnearly total so that very little wave energy is absorbed by the drivesystem.

To quantify the top drive induced absorption of wave energy, SPE 18049defines a complex and unitless reflection coefficient r for torsionalwaves at the interface between the tool string and the drive system asfollows:

$\begin{matrix}{r = \frac{\zeta - Z}{\zeta + Z}} & (1)\end{matrix}$

where ζ is the characteristic impedance of the tool string for torsionalwaves, having unit [(Nm*s)/rad] and Z is the impedance of the drivesystem (in the article this is a rotary table), having unit[(Nm*s)/rad].

Please note the definition of mechanical impedance in formula (1) astorque divided by speed. This in contrast to the reverse definition ofmechanical impedance as speed divided by torque with units [rad/(Nm*s)]used by default in the description of the present invention (unlessreferring to SPE 18049).

Formula (1) is general and applies to all kinds of transmission lines.For instance, note the comparison to impedance matching betweencomponents in electrical engineering to prevent reflections. Thereflection coefficient r is a complex function where, in general, boththe magnitude and phase vary with frequency. If the speed control of thedrive system is stiff (i.e. drive output impedance |Z|>> tool stringcharacteristic impedance ζ), both in units [(Nm*s)/rad], then thereflection coefficient r approaches −1 and substantially 100% of thetorsional wave energy is reflected back down the drill string at thedrive system. The value of r can also reach +1 if the drive is tuned asa stiff torque controller (i.e. drive output impedance |Z|<< tool stringcharacteristic impedance ζ). Still, substantially 100% of wave energywould be reflected at such drives. On the other extreme, if the speedcontrol of the drive system can make the impedance of the drive systemmatch the impedance of the tool string (i.e. Z≈ζ), then the reflectioncoefficient r approaches 0, and ideally 100% of the torsional waveenergy will be absorbed in the drive system. The latter would imply thatsubstantially 0% of the wave energy will be reflected back into the toolstring where such energy might otherwise accumulate and increase theamplitude of vibrations.

SPE 18049 proposes to mitigate stick-slip vibrations by torque feedback.The rotary speed demanded from the drive system (i.e. the set rotaryspeed) is adjusted in response to variations in the torque level. Ameasured torque T is multiplied by the drill string impedance ζ, whichis to be subtracted from the set speed of the drive system. A speedcorrection factor Ω₁, having unit [rad/s], is proportional to minus themeasured torque:

$\begin{matrix}{\Omega_{1} = {{- {HT}} \cong {- \frac{T}{Z}}}} & (2)\end{matrix}$

where H is the torque feedback constant, with unit [rad/(Nm*s)]. Thecorrection allows the drive system speed to respond to dynamic torqueoscillations in such a way that the drive system absorbs or dampens thevibrations. The demanded speed is adjusted in response to variations inthe torque level. When a positive torsional wave travelling up the drillstring meets the drive system, the measured torque increases and therotary speed adjusts slightly. Normally, a control system would react tothe speed dropping below the demanded speed by adjusting the drivetorque output. As pointed out above, this process would reflect most ofthe torsional energy back down the tool string. This reaction issoftened by decreasing the demanded speed in response to an increase intorque.

In the torque feedback system of SPE 18049, however, the effectiveimpedance Z, having unit [(Nm*s)/rad], with torque feedback is:

$\begin{matrix}{Z = \frac{Z_{c\;} + {{i\omega}\; J}}{1 + {HZ}_{c}}} & (3)\end{matrix}$

where

$Z_{c} = {R + \frac{S}{i\; \omega}}$

represents the part of the impedance determined by the speed controllerelectronics and where co represents frequency. I.e., co representsfrequency F of the torsional waves.

The part of formula (3) related to the rotational inertia J of the drivesystem, having unit [kg*m²], renders the feedback system of SPE 18049dependent on frequency ω (or F) of the torsional waves. In consequence,it is impossible to match the drive system impedance Z to the impedanceζ of the drill string for all frequencies. No matter how the speedcontrol electronics tune the impedance part Zc, it is impossible toeliminate wave reflections for all frequencies of the torsional wavesdue to the frequency dependent component related to the inertia J and/orstiffness S of the drive system.

This is confirmed in attached FIGS. 1 and 2, which are derived fromFIGS. 1 and 2 of SPE 18049 respectively.

FIG. 1 shows the amplitude of the reflection coefficient r versusfrequency F in Hertz for various settings 100, 102, 104, 106 of thesystem of SPE 18049. At or near the frequency of the first resonancemode of the tool string, the system can substantially achieve between 10to 80% reduction of the reflection of a torsional wave at said firstresonance frequency. However, for all higher resonance modes, i.e.torsional waves having a higher frequency such as harmonics, thereflection coefficient is significantly higher, i.e. closer to 1,corresponding to considerably less damping.

Waveguide systems may be have either closed/closed, open/open oropen/closed at opposite ends. If only one frequency, i.e. only onewavelength, is being targeted in any given waveguide system, then higherorder frequencies (overtones, harmonics) will still grow, in particularin the absence of standing wave growth at the fundamental frequency.These overtones will be ⅓, ⅕, 1/7, 1/9 etc. times the fundamentalwavelength for an open/closed system. They will be ½, ⅓, ¼, ⅕ etc. timesthe fundamental wavelength for a open/open, or for a closed/closedsystem.

FIG. 2 shows the rotary torque T versus frequency F with (line 122)torque feedback system and without (line 120). F relates to thefrequency of torsional waves. The feedback-system of SPE 18049 is ableto achieve a four-fold reduction of the rotary torque at the frequencyof the lowest mode. The corresponding reduction of reflections at highermodes, however, is much smaller.

In the system disclosed in SPE 18049, the objective of minimizing thereflection coefficient can only be met partly, and only at oneparticular frequency. Rather than neutralising the top drive inertia J,the authors actually use the inertia together with speed controllerstiffness S, to tune the system towards a particular frequency. Asdisclosed in SPE 18049, the reflection coefficient has a minimum for thefrequency, i.e. for a torsional wave having said frequency, making thetop impedance Z purely real (halfway page 3 right column), i.e.2*n*f=√(S/J).

From formula (7) it can be seen what whoud happen if Zc would be broughtto infinite. In that case, Z=1/H, which is the desired zero reflectionsproperty. If Zc were brought close to infinite, the resistance R (orstiffness S) of the drive system is brought to infinite, and S (or R)becomes irrelevant. One can thus no longer tune to a desired frequencyby tuning the value of S.

The objective for the system and method disclosed in SPE 18049 is to(only slightly) lower the wave reflection coefficient at the interfacebetween drillstring-to-topdrive. As indicated by formula (3), theauthors assume a given basic speed controller (such as aproportional-integral controller or PI controller) with sub-optimal Pand I gains (indicated by R and S, also known as damping Cf andstiffness Kf in later publications). Then the authors explain what wouldhappen, which reflection coefficients would be realised by a top drivein combination with such a sub-optimal speed controller. The aboveindicates the constraints of the controller architecture, which has onlythe parameters R, S and H as variables. SPE 18049 links the value for S(Kf) to the value of drive system inertia J to tune the system towards aselected drill string eigenfrequency. In other words, the systemdisclosed in SPE 18049 is tuned towards an observed or predicted toolstring eigenfrequency (or fundamental wavelength).

Consequently, implementations based on the method of SPE 18049 (such aspatents U.S. Pat. No. 5,117,926 and EP-2364397-B1) all require some typeof tuning towards the most problemetic stick-slip frequency, usually thelowest tool string mode, also known as fundamental string frequency.Said frequency may be either observed, e.g. as the period of stick-sliposcillations during drilling, or it can be predicted from the materialand dimensions of the tool string and downhole components.

EP-2364397-B1 discloses a method and system for mitigating stick-sliposcillations, wherein the rotational speed is controlled using a PIcontroller that, when considered together with drive rotational inertiaJ, is tuned to a selected stick-slip frequency, so that the drive systemabsorbs torsional oscillations at or near said selected frequency.

In the system and method of EP-2364397-B1, the I-term of the PIcontroller is adjusted according to I=ω_(s) ²J with units [Nm/rad],where ω_(s) is an approximate or estimated angular frequency of saidstick-slip oscillations and J is the effective inertia of the drivesystem. Disadvantages thereof include the limitation to the selectedfrequency. Waves at other frequencies, including harmonics of theselected stick-slip frequency, will still be partly reflected, therebypossibly increasing in amplitude and evolving into standing wavesreflected at both ends of the drill string. But most importantly, as thereflection coefficient provided by the system of EP-2364397-B1 willalways be greater than 0, standing waves can still emerge, although itmay take longer before the resonance has reached enough amplitude forthe bit speed to approach zero, at which point it stalls (sticks), andneeds substantially more torque before it will start to rotate again ina shock.

The prior art methods referenced above all provide some improvement inthe stick-slip free operating envelope of the system.

The present invention aims to provide an improved method and system formitigating vibrations.

The invention therefore provides a method of damping vibrations in atool string, said vibrations comprising torsional waves propagatingalong said tool string, the method comprising the steps of:

-   -   instructing a drive system to rotate the tool string at a set        rotational speed;    -   determining a rotational speed of the tool string;    -   determining a torque at or near the interface between the tool        string and the drive system;    -   determining a tool string impedance of a tool string section        adjacent said interface;    -   calculating a rotation correction signal using the determined        torque multiplied by the determined tool string impedance;    -   correcting the set rotational speed using the rotation        correction signal to provide a corrected set rotational speed        signal;    -   subtracting the measured rotational speed from the corrected set        rotational speed signal to provide a twice corrected set        rotational speed signal to the drive system.

The method of the invention comprises a first correction signal, whichmatches the impedance of the drive system to the impedance of the toolstring connected to the drive system. The correction signal adjusts theimpedance of the drive system as observed by a wave propagating alongthe tool string towards the drive system. The method combines theimpedance correction signal with a second control signal to tune therotational speed of the tool string to the rotational speed as set bythe impedance matched correction signal. The latter feedback loop urgesthe drive system to accurately follow the impedance matched controlsignal, which in effect ensures that the drive system inertia, asobserved by the wave propagating along the tool string towards the drivesystem, approaches zero. Thus, the effective impedance Z can be madefrequency independent.

As a result, the wave will be absorbed for all frequencies, in line withactive impedance matching theory as commonly applied intelecommunications transmission line electronic drive circuitry. Inpractice, for all frequencies herein may imply all frequencies within aselected frequency band. The selected frequency band for instancecomprises a plurality of reflection modes, also known as harmonics orovertones.

In an embodiment, the method may be set to function within a range ofenvisaged stick-slip frequencies.

In another embodiment, the method includes steps for automatic tuningthe determined tool string impedance. The embodiment obviates the needfor re-tuning the system every time a section of tool pipe or rod withdifferent characteristics (different relative to a previously used pipeor rod) is added to the tool string and connected to the drivingelement.

The method can eliminate the first mode as well as higher modes ofoscillation. The method is robust and handles any waves resulting fromchanges in the interaction between, for example, the rock formation andthe drill bit (frictional changes, damping changes, etc), step changesin the rotational speed of the drive system, step changes in bit torque,etc.

In an embodiment, the method may include the step of adding orsubtracting a third corrective speed signal to or from the twicecorrected set rotational speed signal. This ensures that, at timescalesmuch longer than the longest expected stick-slip period, the tool stringrotational speed is eventually adjusted to the desired set point speed.

According to another aspect, the invention provides a control system fordamping vibrations in a tool string, said vibrations comprisingtorsional waves propagating along said tool string, the systemcomprising:

-   -   a user control module for instructing a drive system to rotate        the tool string at a set rotational speed;    -   a sensor for determining a rotational speed of the tool string;    -   a torque sensor for determining a torque at the interface        between the tool string and the drive system;    -   a processing unit for determining a tool string impedance of a        section of the tool string adjacent said interface;    -   a first feedback loop comprising means for multiplying the        torque by an impedance gain factor, which impedance gain value        is set to correspond to a tool string impedance, for providing a        rotation correction signal, and for correcting the set        rotational speed using the rotation correction signal to provide        a corrected set rotational speed signal;    -   a second feedback loop for subtracting the determined rotational        speed from the corrected set rotational speed signal to provide        a twice corrected set rotational speed signal to the drive        system.

In an embodiment, the tool string may drive a bottom hole assembly of adrilling device. In another embodiment, the tool string may drive a pumpdevice.

Herein, please note the reversed definition of mechanical impedanceusing speed divided by torque. I.e., by default the description of thepresent invention will use a reverse definition of mechanical impedance,wherein mechanical impedance is defined as speed divided by torque,having unit [rad/(Nm*s)].

In an embodiment, the system includes a third feedback loop. The thirdfeedback loop ensures that, at timescales much longer than the longestexpected stick-slip period, the tool string rotational speed is adjustedto the desired set point speed, irrespective of the static torque thatneeds to be supplied by the drive.

The invention will be described hereinafter in more detail by way ofexample, with reference to the drawings, in which:

FIG. 1 shows a graph indicating amplitude of reflection coefficient rversus frequency of oscillations for various prior art control systems,and for a control system of the invention;

FIG. 2 shows a graph indicating amplitude of the drive torque versusfrequency of oscillations for some prior art control systems, and for acontrol system of the invention;

FIG. 3 shows a drilling system to be controlled by the method andcontrol system of the invention;

FIG. 4 shows a schematic setup of the drilling system including acontrol system of the invention;

FIG. 5 shows a prior art control system; and

FIGS. 6 to 11 show embodiments of a control system of the invention.

In the description, like reference numerals relate to like components.

FIG. 3 shows a drilling system 1 including a drilling rig 10 and a drillstring 12 suspended from said rig at surface into a borehole (not shown)formed in an earth formation. The drill string 12 can be relativelylong, and may have a length of several kilometers or more. The drillstring typically comprises lengths of drill pipe 14 screwed together endto end. The drilling rig 10 may be any sort of oilfield, utility, miningor geothermal drilling rig, including: floating and land rigs, mobileand slant rigs, submersible, semi-submersible, platform, jack-up anddrill ship.

A bottom hole assembly (BHA) 16 may be provided at the downhole end ofthe drill string 12. The bottom hole assembly (BHA) 16 may include oneor more sections of drill collar and/or heavy weight drill pipe, eachhaving an increased weight with respect to the drill pipe sections 14,to provide the necessary weight on bit during drilling. In addition, theBHA 16 may comprise a transmitter 18 (which may be for example awireline telemetry system, a mud pulse telemetry system, anelectromagnetic telemetry system, an acoustic telemetry system, or awired pipe telemetry system), centralisers 20, a directional tool 22(which can be sonde or collar mounted), stabilisers (fixed or variable)and a drill bit 28.

The drilling rig 10 comprises a drive system 30. During drilling, thedrill string 12 together with the BHA and the drill bit is rotated bythe drive system 30. The function of the drive system 30 is to rotatethe drill string 12 and thereby the drill bit 28 at the downhole endthereof. In case a downhole motor or turbine is used, drill stringrotational speed is (much) lower then bit rotational speed.

Presently most drilling systems include so-called top drives. However,some drilling rigs use a rotary table and the invention is equallyapplicable to such rigs. The invention is also equally useful indrilling any kind of borehole e.g. straight, deviated, horizontal orvertical.

A pump 32 may be located at the surface. During drilling operation, thepump 32 typically pumps drilling fluid through the drill string 12 andthrough the drill bit 28. The drilling fluid cools and lubricates thedrill bit during drilling, and returns cuttings to the surface via theannulus formed between the drill string 12 and the wellbore wall (notshown).

The system may include a user control unit 34. Drilling data andinformation may be displayed on a screen 36 of the control unit 34. Thecontrol unit may typically include a user input device such as akeyboard (not shown) for controlling at least part of the drillingprocess. A logic controller 38 sends and receives data to and from theconsole 34 and the top drive 30. In particular, an operator may be ableto set a speed command and a torque limit for the drive system tocontrol the speed at which the drill string rotates.

As shown in FIG. 4, the controller 38 may comprise a memory unit 40,such as a battery backed-up RAM or flash memory. The memory may storecomputer executable instructions that, when executed, perform thefunction of a speed controller 42 for the top drive 30. Alternatively,part or all of said executable instructions may be implemented inhardware. In the embodiment shown in FIG. 4, the speed controller 42 isseparate and distinct from the drive system 30. However, it is possiblefor the functionality of the speed controller to be provided as part ofa built-in dedicated speed controller of a top drive.

The motor for driving the tool string 116 may include an electric motor30. Optionally, a shaft of the motor 30 can be coupled to the rod string12 through a gearbox 36 or similar speed reduction mechanism.Alternatively, the motor may be controlled by a variable frequency drivesystem (See for instance FIG. 5).

The motor 30 can be a three-phase AC induction motor designed to beoperated from line voltages in the range of 230 VAC to 690 VAC anddeveloping 5 to 250 horsepower, depending upon the capacity and depth ofthe pump. The gearbox 36 may convert motor torque and speed input to asuitable torque and speed output for driving the rod string 12 and helix14.

In use, the tool string 12 together with the helix 14 of the pump 16 isrotated by the drive system 30.

The system typically includes a user control unit 34. Data andinformation may be displayed on a screen 36 of the control unit 34. Thecontrol unit may typically include a user input device such as akeyboard (not shown) for controlling at least part of the process. Alogic controller 38 sends and receives data to and from the console 34and the drive system 30. In particular, an operator may be able to set aspeed command and a torque limit for the drive system to control thespeed at which the tool string 12 rotates.

As shown in FIG. 4, the controller 38 may comprise a memory unit 40,such as a battery backed-up RAM or flash memory. The memory may storecomputer executable instructions that, when executed, perform thefunction of a speed controller 42 for the motor 30. Alternatively, partor all of said executable instructions may be implemented in hardware.In the embodiment shown in FIG. 4, the speed controller 42 is separateand distinct from the drive system 30. However, it is possible for thefunctionality of the speed controller to be provided as part of abuilt-in dedicated speed controller of a motor or similar drive system.

It is to be understood that the system and method of the invention maybe implemented into other control systems or as a separate component.The pump control system 4 controls the operation of the pump 16. Thepump control system 4 may include transducers, such as motor current andmotor voltage sensors, to sense dynamic variables associated with motortorque and velocity. Current sensors may be coupled to a sufficientnumber of the motor windings, for instance two in the case of a threephase AC motor. Voltage sensors may be connected across the motorwinding inputs. The motor current and voltage signals produced by thesesensors may be supplied to a processing unit 38 of the controller 4through suitable input/output devices. The storage unit 40 may havememory that is volatile (such as RAM), non-volatile (such as ROM, flashmemory, etc.) or some combination of the two.

FIG. 5 shows a schematic representation of a prior art system, which isfor instance suitable for implementing a torque feedback system asdisclosed in SPE 18049. User control unit 34 is connected to a so-calledproportional and integral (PI) controller 140. The PI controller isconnected to a motor management system 142, for instance a variablefrequency drive (VFD) unit, which controls motor 144. The motor 144 isconnected to an uphole end of the tool string 12, which is provided withequipment at the opposite downhole end. A rotational inertia J of thedrive system is schematically represented by inertia block 146 at theinterface between the tool string 12 and the drive system. Herein, J isthe rotational inertia that constitutes a substantial part of the driveimpedance. The drive impedance is the impedance that is encountered by awave propagating via the drill string and arriving at the interfacebetween the drive system and the drill string. A sensor 148 detectsrotational speed ω_(r) (for instance in rotations per minute (RPM) orrad per second). The motor management unit 142 is able to monitor motortorque Tm. Said motor torque Tm may for instance be made available to anoperator via the user interface of control unit 34.

In use, the sensor 148 provides the measured rotational speed ω_(r), forinstance having unit [rad/s], to an input of sum element 150, whichsubtracts the measured rotational speed ω_(r) from the set rotationalspeed Ω, for instance having unit [rad/s], as set by the operator. Theoutput 152 of the sum element 150, comprising the differentialrotational speed Ω_(cif), is provided to the PI controller 140. I.e.,the sum element will provide an input signal to the PI controller whenthe rotational speed of the drill string differs from the set rotationspeed.

As described above, the unit of ω_(r), as provided by sensor 148, is anangular speed in rad/s. If measured in RPM then said angular speed maybe multiplied by 2*π/60 to get rad/s. Subsequently it can be used asdescribed in the control and flow diagrams of the respective Figures andthe corresponding description.

Embodiments of the system according to the invention will be describedbelow. Features and components which have been described before willhave the same reference numbers and will not be described again.

FIG. 6 shows an embodiment for a feedback system according to theinvention. Torque sensor 160 measures torque T_(d), having unit [Nm],delivered to the tool string 12. The sensor 160 is preferably located ator near the interface between the motor 144 and the uphole end of thetool string. The output 162 of the torque sensor, providing measuredtorque T_(d), is coupled to the input of amplifier 164. The amplifier164 may amplify the input signal by a predetermined gain, for instancez′. Herein, z′ may be set to correspond to ζ, which is thecharacteristic tool string impedance (unit [rad/(Nm*s)]). The relevanttool string impedance herein is the impedance of the top section of thetool string, i.e. the section which is connected to the drive system.

The torsional impedance of the tool string is a frequency independentvalue, which can be calculated. For instance using the formula:

$\begin{matrix}{\zeta = \frac{1}{\frac{1}{32}*\pi*( {{OD}^{4} - {ID}^{4}} )*\sqrt{G*\rho}}} & (4)\end{matrix}$

(ζ in unit [rad/(Nm*s)]), with inner diameter ID and outer diameter OD,shear modulus G and density ρ of the material of the tool string.Formula (4) is valid for a tool string including an inner fluid channelhaving diameter 2*ID, as well as for a solid tool string. For a solidtool string, ID=0.

Thus, the output of amplifier 164 forms a speed correction signal 190,with unit [rad/s], which is provided to sum element 166.

Set rotational speed Ω_(r), as set by the operator via user control unit34, is provided to gain module 168, and multiplied by a gain factor G.Said gain factor is for instance 2. The amplified set rotational speedG*Ω_(r) is provided to another input of sum element 166. The sum element166 subtracts the calculated speed correction signal 190 from theamplified set rotational speed, and provides the corrected setrotational speed Ω_(r,cor) to an input 170 of sum element 150. Herein:

Ω_(r,cor)=2*Ω_(r) −T _(d) *z′  (5)

The units of Ω_(r) and Ω_(r,cor) are in [rad/s]. The unit of z′ is[(rad/s)/N*m]=[rad/(Nm*s)]. The unit of torque is [N*m].

The sum element 150 subsequently subtracts the measured rotational speedω_(r), as provided by the sensor 148, from the corrected set rotationalspeed Ω_(r,cor), to provide a twice corrected rotational speedΩ_(r,2cor) [rad/s]:

Ω_(r,2cor)=Ω_(r,cor)Ω_(r)=2*Ω_(r) −T _(d) *z′−Ω _(r)   (6)

The sum element 150 provides the twice corrected rotational speedΩ_(r,2cor) to the PI controller 140, indicated by signal 172.

The objective of the controller is to bring the twice correctedrotational speed Ω_(r,2cor) to zero, so that formula (6) provides:

Ω_(r,2cor)=2*Ω_(r) −T _(d) *z′−Ω _(r)=0

or

$\begin{matrix}{z^{\prime} = \frac{( {{2*\Omega_{r}} - \omega_{r}} )}{T_{d}}} & (7)\end{matrix}$

Formula (7) does not include a component which depents on the frequencyof torsional waves. Formula (7) lacks a frequency dependent component,and z′ is a purely real and frequency independent value. Purely realherein means that z′ lacks a complex part. Also, please note thatω_(r)in formula (7) relates to the (measured) rotational speed of thetool string. This is contrary to formula (3) above, which is derivedfrom SPE 18049 and uses the symbol ω to represent frequency of atorsional wave.

As a result, the system of the invention enables the damping of allvibrational modes, for instance over a selected frequency range, usinggain value z′ in a feedback loop, wherein z′ is a real and frequencyindependent value. Said frequency range relates to frequencies of thetorsional waves. The frequency range may include the fundamentaltorsional wave frequency and any predetermined number of harmonicsthereof.

The PI controller may function as a typical stiff PI controller,obviating the need to tune the controller 140 to any specific(resonance) frequency. Said PI controller may be simplified further to amore basic P-only controller, with its value P set as high as possible,limited only by dead time and sensor/actuator phase errors within thecontrol loop. The remainder of the system functions as described before.

Referring to formula (3) above, in the system of the invention, thecontroller gain Zc may be set as high as possible without loosingcontroller loop stability, and then dampen any torsional vibrations.

In a practical embodiment, the speed controller 140 is a stiff speedcontroller. Stiff controller herein implies that the speed controller140 has a gain set at relatively (very) high values. The gain ispreferably set at infinite. In practice, the gain may be in the order of10,000 Nms/rad or (much) more. The gain may be set at, for instance,15,000 Nms/rad, 20,000 Nms/rad, 50,000 Nms/rad, or more. Setting thegain of the speed controller at a relatively high value in combinationwith the feedback mechanism of the invention improves the frequencyindepence of the vibration damping.

Gain of the speed controller herein refers to one or more of theproportional, integral and/or derivative terms of a PI or PIDcontroller. The PID control scheme is named after its three correctingterms, whose sum constitutes the manipulated variable (MV). Theproportional, integral, and derivative terms are summed to calculate theoutput of the PID controller. The system of the invention may include aPI controller, which lacks the derivative term. Defining u(t) as thecontroller output, the final form of the PID algorithm is:

${u(t)} = {{{MV}(t)} = {{K_{p}{(t)}} + {K_{i}{\int\limits_{0}^{t}{{(\tau)}{(\tau)}}}} + {K_{d}\frac{}{t}{(t)}}}}$

wherein K_(p) is Proportional gain, K_(i) is Integral gain, K_(d) isDerivative gain, e is an Error, t is Time or instantaneous time (thepresent), T is a Variable of integration, which takes on values fromtime 0 to the present t.

The proportional term produces an output value that is proportional tothe current error value. The proportional response can be adjusted bymultiplying the error by a constant K_(p), called the proportional gainconstant.

A high proportional gain results in a large change in the output for agiven change in the error. If the proportional gain is too high, thesystem can become unstable (see the section on loop tuning). Incontrast, a small gain results in a small output response to a largeinput error, and a less responsive or less sensitive controller. If theproportional gain is too low, the control action may be too small whenresponding to system disturbances. Tuning theory and industrial practiceindicate that the proportional term should contribute the bulk of theoutput change.

The contribution from the integral term is proportional to both themagnitude of the error and the duration of the error. The integral in aPID controller is the sum of the instantaneous error over time and givesthe accumulated offset that should have been corrected previously. Theaccumulated error is then multiplied by the integral gain (K_(i)) andadded to the controller output.

The integral term accelerates the movement of the process towardssetpoint and eliminates the residual steady-state error that occurs witha pure proportional controller. However, since the integral termresponds to accumulated errors from the past, it can cause the presentvalue to overshoot the setpoint value.

The derivative of the process error is calculated by determining theslope of the error over time and multiplying this rate of change by thederivative gain Kd. The magnitude of the contribution of the derivativeterm to the overall control action is termed the derivative gain, K_(d).

According to the invention, the gain of the speed controller 140 may beset relatively high, providing a relatively stiff speed controller. Gainherein may include one or more of the Proportional gain (K_(p)), theIntegral gain (K_(i)), and the derivative gain (K_(d)). Preferably, atleast the Proportional gain (K_(p)) is set relatively high. Relativelyhigh herein may indicate 10,000 Nms/rad or more in practice.

In another embodiment, as shown in FIG. 7, the pipe torque is calculatedfrom the sensed motor torque Tm and the measured speed ω_(r). The motortorque Tm from the motor management unit 142 is provided to an input 180of sum element 182. Another input 184 of said sum element 182 isprovided with a speed dependant torque signal T(ω_(r)). Said torquesignal is the result of the measured rotational speed ω_(r) provided todifferentiator 186 and to amplifier 188. Said amplifier amplifies thedifferentiated rotational speed by a gain factor, which may besubstantially equal to the rotational inertia J of the drive system:

$\begin{matrix}{{T( \omega_{r} )} = {J*\frac{}{t}\omega_{r}}} & (8)\end{matrix}$

Herein, T(ω_(r)) [Nm] approximates the torque required to accelerate anddecelerate the rotational inertia J of the drive system and d/dt(ω_(r))[rad/s²] is an approximation of said acceleration.

The sum element 182 subtracts the speed dependant torque signal T(ω_(r))from the motor torque Tm:

T _(cor) =T _(m) −T(ω_(r))   (9)

Herein, T_(cor) is an approximation of the tool string torque Td asshown in FIG. 6.

The corrected torque signal T_(cor) is multiplied by a factor z′. Hereinz′ is the desired output impedance of the drive system. The outputimpedance of the drive system would be indicated by z. The value of z′may be set substantially equal to the impedance ζ of the tool string.Using the same procedure as laid out in the embodiment of FIG. 6, thisresults in the amplified set rotational speed Ω_(r,cor) which isprovided to sum element 150. In formula:

$\begin{matrix}{\Omega_{r,{cor}} = {{{2*\Omega_{r}} - {( {T_{m} - {T( \omega_{r} )}} )*z^{\prime}}} = {{2*\Omega_{r}} - {( {T_{m} - {J*\frac{}{t}\omega_{r}}} )*z^{\prime}}}}} & (10)\end{matrix}$

Formula (10) effectively replaces formula (5), which was related to theembodiment of FIG. 6. It is an option to use the commanded motor torque(the signal from 140 to 142), instead of the sensed motor torque Tm.

In an improved embodiment, shown in FIG. 8, the rotational speed sensor148 has a limited bandwidth. The bandwidth is limited to a range havingthe lowest noise level. To limit noise to propagate through the controlsystem, a low pass filter 200 is provided to the output of speed sensor148. The motor torque Tm is provided to low pass filter 202. Filter 202aims to mimic the behaviour of filter 200. Filter 202 also mimicsbehaviour of low pass filtering and dead time that might exist withinthe torque actuator (i.e. the motor) to speed sensor signal path, sothat subtracting the outputs of filters 200 and 202 later on will notintroduce artefacts that may lead to instabilities. The corrections fromthe rotational speed will be limited to an upper frequency, which willform an upper limit for the primary and multi-mode stick-slipfrequencies to be eliminated. In practice, the low pass filters 200 and202 may have a cut-off frequency of about 5 Hz.

Likewise, for optimised performance with highest proportional gain P (ofthe PI controller 140) possible, the intrinsic low pass filtering anddead time in the motor and the motor management system (whether DC orvariable frequency AC drive or hydraulic) are preferably mimickedelectronically in the torque feedback signal path to summing block 182.

In an improved embodiment, shown in FIG. 9, the system includes sumelement 204, amplifier 206 and integrator 208. The embodiment of FIG. 9has improved ability to hold and control the time averaged tool stringspeed at the speed Ω_(r) as set by the operator under different torqueloads. In addition, the embodiment prevents the drive system to stall atrelatively low torque levels.

The filtered rotational speed ω_(r) is provided to an input of the sumelement 204, and subtracted from the set rotational speed Ω_(r). Thedifferential rotational speed Ω_(r,dif) is multiplied by the amplifier206, for instance by a factor k. Herein, k sets a radial transitionfrequency [rad/s], indicating (when combined with a given impedance Z) afrequency whereat the system makes a transition from a stiff controllerto an impedance matched controller. Optionally, a cut-off frequency k′may be set in [Hz]. Then, the factor k will be k=(2π)*k′[rad/s].

The multiplied differential rotational speed is integrated by integrator208. The integrator provides any changes in the multiplied differentialrotational speed to an additional input 210 of the sum element 166,which adds the latter to the multiplied set rotational speed 2*Ω_(r).The assembly of amplifier 206 and integrator 208 functions as a low-passfilter. Herein, below a set lower threshold frequency determined by k,the system will urge the tool string 12 to follow the set rotationalspeed exactly regardless of the torque load. In other words it enablesthe system to achieve a correct setpoint speed, wherein the zerofrequency component is excluded from the active impedance matchingfeedback process.

In a practical embodiment, the transition frequency is in the order ofabout 0.02 to 0.1 Hz.

Yet another improvement enables the system to automatically determinethe correct impedance multiplication factor z′ of multiplier block 164to achieve the aimed impedance matching. Such an automatic adjustmentobviates the need for manual entry of tool string characteristics.Automatic adjustment improves accuracy, is more user friendly and lesslabour intensive. In addition, it will provide more accurate resultsbecause changes in tool string diameters, for instance due to lifecyclewear and corrosion, and influences of the complex geometry of tooljoints and upsets on tool string impedance ζ are also taken intoaccount.

In view of the above, the validity of generic torsional impedanceformulas as often used in literature, such as formula (4) above, mayhave limitations when applied in practice. The invention allows toautomatically set the correct value of z′ in block 164 so that at thedrive system end of a tool string, torsional waves originating fromdownhole will not bounce back into the borehole.

One method for automatically matching the drive system impedance z to(top) tool string impedance ζ is to determine the magnitude of impedancemismatch by observing the effect on top drive RPM immediately after astep change in RPM setpoint. Electronic transmission line literaturesuggests that a perfectly matched source impedance would show a ratio of50%. With the multiplication of the RPM setpoint set at 2, as shown inthe embodiments of FIG. 6 and further, the ratio will be 100%.

Thus, if immediately after a setpoint step, the ratio in observed stepamplitudes between surface RPM and setpoint RPM is greater than 1, aninitially estimated impedance gain value z′ in block 164 will beincreased. If said ratio is lower than 1, then impedance gain value z′will be decreased. Thus, without upfront knowledge of connected toolstring characteristics the optimum gain value for z′ to be programmed inblock 164 can be found automatically. The method may use a number ofsubsequent steps of successive approximation, for example 6 to 10 stepsof successive approximation.

This method is immune to scaling errors in both the torque and in thespeed sensor paths in as far these signals would need to be calibratedin engineering units. Impedance can be considered ‘matched’ whenrotation speed halves after connecting a load of equal impedance. In thecase of tool string, it is preferred that its impedance is sensedimmediately after each setpoint step, long before echoes from aconnected BHA or open or fixed end have bounced back to the sensors atsurface. Because torsional waves may travel at approximately 3 km/s,this would, for example, need to be within 1 second if a 1.5 km longhomogeneous tool string were used.

An improved method for automatically matching drive impedance z to (top)tool string impedance ζ is shown in FIG. 10. Using a telecommunicationcable diagnostic technique of time domain reflectometry, a spatial imageof transmission line impedance changes can be acquired from signals atone end of a long cable. Similarly, an image of a tool string includingthe coupling to a drive, can be derived from torque and rotational speedsignals. These images show a positive peak at the origin (at timet=0[s]) if the drive system impedance z is less than the load impedance(i.e. the tool string impedance ζ), and a negative peak if the drivesystem impedance z is higher than the tool string impedance ζ. The peakis absent when the impedance is matched (i.e. z≈z′≈ζ). Therefore, bysuccessively measuring the sign of the peak in time domain reflectometryfunctions, and adjusting an estimated value for impedance gain value z′of amplifier 164 either up or down, the estimated value z′ can be tunedautomatically to substantially precisely match the tool string impedanceζ.

White noise generator 216 provides a white noise signal 218 to sumelement 220. The white noise signal may have units [rad/s]. The sumelement 220 adds the white noise signal 218 to the set rotational speedΩ_(r). The signal 221, comprising the sum of the set rotational speedΩ_(r) and the white noise, is provided to the amplifier 168 and to thesum element 204.

The same white noise signal 218 is also provided to a first input,marked A, of a cross correlator unit 222. A second input, marked B, ofthe cross correlator unit 222 is provided with the difference of themeasured rotational speed 149 (ω_(r)) and the output of gain block 164,as provided by sum element 226. The cross correlator unit 222 is adaptedto provide a cross-correlation function, from which signal 224 isderived. The multi-channel cross-correlation time signal 224 is forinstance provided periodically and may be calculated from:

S _(ccf)=IFFT(FFT(A)*CONJ(FFT(B)))   (11)

wherein FFT means fast fourier transform (an algorithm to compute adiscrete Fourier transform (DFT)), IFFT means inverse fast fouriertransform, and CONJ means the conjugate operation.

Signal 224 covers the average correlation coefficients in a time windowfrom −t to t, wherein t is chosen such that reflections from the BHA areexcluded because these can be assumed too far away in the spatial domainand thus also in the time domain. Torsional waves in tool string maytravel at approximately 3 km/s, so that t would, for example, need to bewell below 1 second if a 1.5 km long homogenous tool string were used.

Signal 224 contains only information on the part of the tool stringimage that belongs to the drive system and to the first few hundredmeters near the uphole end of the tool string. Heavy weight tool stringpipe, and optional other components such as drill collars, bit, andhelical blade 14, are thus invisible in signal 224 (channels −t to t),but the impedance change from drive system to tool string is visible.Signal 224 shows a positive value if the drive impedance z is less thanthe source impedance, and a negative value if the drive impedance ishigher. The value is zero when the impedance is perfectly matched.Signal 224 can thus be used to feed an integrator 232. The output 234 ofsaid integrator 232 automatically tunes to and then holds the optimumvalue for z in block 164. Said cross correlation signal 224, mayoptionally be presented on a driller console graphic display as a fullimage of impedance changes across the toolstring depth, and thus, forexample, assist drillers in estimating the depth of stuck drill pipe orproblematic stabiliser to wall friction points in the borehole.

The integration operation functions as a form of first-order low-passfilter, which can be performed in the continuous-time (analog) domain orapproximated (simulated) in the discrete-time (digital) domain. Theintegrator may have a low pass filtering effect.

In a practical embodiment, the amplitude of the white noise may be about3 to 10%, for instance about 5%, of the amplitude of the set rotationalspeed Ω_(r) signal as provided by the user control unit 34.Alternatively, the added noise amplitude may be selected at about, forexample, 10 RPM rms (root mean squares) while the set rotation speed (asselected by unit 34) is kept at zero. A frequency spectrum of the whitenoise signal 218 may be limited to a preselected frequency range, forinstance having similar cut-off frequencies as the high-pass circuit(amplifier 206 in combination with integrator 208) and low-pass filters200, 202. Said frequency range is for instance about 0.1 to about 5 Hz.Herein, the lower and upper cut-off frequencies may be adjusted,depending on the expected or observed range of resonance frequencies inthe tool string 12 and the limitations of the drive such as bandwidthand dead time of the motor and motor management system and bandwidth ofthe sensor(s) used.

The integrator 232 may be truncated at upper and lower limits dependingon minimum and maximum drill string dimensions. Herein, the tool string12 may typically comprise connected tool string sections. A typicaldrill pipe may have a length of about 31 foot (˜10 m) and a specifiedoutside diameter (e.g. 3½ inch, 4 inch, 5 inch, 5½ inch, 5⅞ inch, or 6⅝inch (about 8.9 to 17 cm)). Tool string sections are generally providedwith an internal fluid conduit, for instance having an inner diameter inthe order of 1 to 6 inch (about 2.5 to 15 cm). The integrator 232 maytherefore be truncated accordingly, for instance between 1/33 and 1/1000rad/(Nm*s).

An operator of the system may choose how often and how fast thisautomatic impedance matching should be performed.

FIG. 11 shows an embodiment including a section to enable automaticsensing of the drive system rotational inertia J (as represented byblock 146). Knowledge of this inertia value becomes relevant inembodiments where torque signal 162 cannot be derived directly from atorque sensor 160, for instance because such a toolpipe torque sensormay not be available.

Neglecting transmission losses, the equation of motion of the drivesystem output shaft is:

$\begin{matrix}{{J*\frac{}{t}\omega_{r}} = {T\mspace{11mu}\lbrack{Nm}\rbrack}} & (12)\end{matrix}$

where J is the effective drive system inertia (including gear and drivemotors) and T is the torque in [Nm] required to accelerate anddecelerate the rotational inertia J and follows from the difference ofthe motor torque Tm and the torque applied to the tool string Ts. If notool string is connected to the system, then torque T will be equal tothe measured motor torque Tm. In practice, the difference between Tm andTs may be slightly higher than the torque T required to accelerate thedrive inertia J and stems from internal viscous or coulomb friction andmay be accounted for. If no drill pipe torque sensor 160 is available tocalculate T from Tm, then the inertia sensing method is best appliedwhen the drive system is unloaded, i.e. without a drill stringconnected. Also please note that the required changing drive systemspeed may be generated from the white noise generator 216 in the sameway as described in the embodiment of FIG. 10.

The inertia sensing section of the system of the invention includes ahigh pass filter 240, a high pass filter 242, and a divider element 244.The differentiated and low-pass filtered rotational speed signal 246,corresponding to a rotational acceleration in [rad/s²], is provided tothe high-pass filter 240. The low-pass filtered motor torque Tm 248 withunits [Nm] and now assumed to be torque T, is provided to the high-passfilter 242. The high-pass filtered signals 250, 252 are provided torespective inputs of the divider element 244, which divides signal 252by signal 250, and outputs an inertia signal 254 from:

$\begin{matrix}{J = {T/\frac{\omega_{r}}{t}}} & (12)\end{matrix}$

The inertia signal 254 is provided to amplifier 188, which uses saidinertia signal as the gain factor thereof. The value J ([kg*m²]) is tobe determined only once prior to putting a system into service. Onlywhen motors or gearboxes are changed, the procedure for determining thevalue of J should be repeated.

Other approaches for automatically determining the value J to beprovided to amplifier 188 include intelligent analysis of a speedsetpoint step response, whereby overshoot or undershoot in the resultingtop drive speed is to be adjusted. Locations at or near surface allowaccurate measurements of parameters using high-frequency sensors.High-frequency implies for instance exceeding 100 Hz.

Uphole rotary velocity ω_(r), torque Tm and/or torque Ts or a relatedparameter may for instance be measured by a sensor at or near surface.Suitable sensors include, for example, tacho generators or opticalencoders, located either upstream or downstream of a gearbox, and(wireless) torque sensors in saver subs or instrumented internal blowoutpreventors (I-BOP) that may be present between a motor and the drillpipe shaft. Said related parameter is for example a time period betweentwo pulses of an optical encoder that measures, for example, 1024 pulsesfor one rotation of the drill string 12 at an uphole location. Theperiod between pulses is directly related to and representative ofangular velocity. Alignment of top drive shafts can be poor, leading tounwanted distortion in sensed rotary velocity signal ω_(r). In a typicalembodiment, the drill string rotational speed signal must be updated atrates far above the shaft revolutions per second rate. Angular dependentscale errors in the speed signal should thus preferably be compensatedfor in real time, for instance, by employing a self populating lookuptable for each of the, for example, 1024 distinct angular encoderabsolute shaft positions.

A driller operates the drilling rig (see FIG. 3) and sets a voltageinput V representative of set rotational speed Ω_(r) via user controlunit 34. In response to the voltage signal V, the drive system 30 willtry to rotate the drill string 12 at the reference rotation Ω_(r). Torotate the drill string, the drive system 30 provides a motor torque Tmto the drive system inertia and the drill string 12. In response to thereceived motor torque Tm, the drill string and drill bit of the drillingsystem will rotate. In the system of the invention, only upholecomponents, which can be accurately measured, are required. Downholemeasurements, at low sample rates, are obviated.

It is for instance sufficient to measure the rotary speed ω_(r) at theconnection between the drive system and the drilling system, forinstance using sensor 148. Sensor 148 may be a separate module, or maybe included in the drive system 30.

The torque Tm can be derived from the current in the drive system 30.Alternatively, for modern AC drives torque signal Tm can be derived fromvariable frequency drive diagnostic outputs or in general from the motormanagement system. Otherwise, Ts can be measured accurately at or nearthe interface between the motor 144 and the tool string 12, for instanceusing sensor 160. The sensor 160 may be part of a wireless instrumentedsaver sub or IBOP (blow out preventer). Furthermore, torque signal Tmcould even be derived by copying the commanded torque signal in between140 and 142.

The system and method of the invention may be combined with the systemand method of U.S. Pat. No. 5,117,926 (commercially available under thename SOFT TORQUE). The combined systems may mitigate torsional waveseven more than each system separately.

The system and method of the invention allow automatic operation. Theonly parameters required are the inertia of the drive system (which isknown or can be automatically sensed, see FIG. 11) and the impedance ζof the top section of a tool string (which may be calculated using toolstring dimensions, see for instance formula (4), or can be determinedautomatically, see for instance FIG. 10). Please note that the impedanceζ is a real value, and is independent of the frequency of a torsionalwave reaching the interface between the tool string and the drive system(see formula (7)). The system resolves resonances across a predeterminedfrequency range, rather than at a single selected frequency.Consequently, at least within said frequency range all waves reachingthe drive system 30 are, at least partly, absorbed.

Referring to FIGS. 1 and 2, lines 108 and 124 indicate reflectioncoefficient r and rotary torque T respectively, when using the system ormethod of the invention. Line 108 indicates that the reflectioncoefficient r is lowered over the entire selected frequency range (i.e.between the set high-pass and low-pass frequencies) rather than at onefrequency only. Line 124 reflects the corresponding result, showing thatall oscillation modes are equally reduced.

The method of the present invention realizes a simple,frequency-independent source output impedance at the drive system whichis observed by all waves that travel upwards via the drill pipe. Thesystem of the invention works, independent of the wavelength oramplitude of the waves, and independent of the inertia of the drivesystem.

Advantages of the method of the invention are:

a) Tuning towards actual drill string length and configuration of theBHA is obviated. The method is therefore easier to use and provides amore robust solution to obviate the problem of stick-slip vibrations;

b) Methods based on automatic tuning for the PI controller 140, such asfor instance pioneered with Bentec and Shell's Mark iii Soft TorqueSystem, NOV's SoftSpeed® II, and others, which typically fail when aliensignals, for instance from offshore drillrig heaves, are present, areobviated;

c) Multiple modes are dealt with in parallel. The system dampensunwanted oscillations at all frequencies within a selected frequencyrange (for instance 0.1 to 5 Hz) at once;

d) Even when torque signals are wrongly scaled, the system can stillwork out how to rescale in order to achieve optimal impedance matching.

The term “uphole” may refer to locations at surface or above surface(e.g. from the seabed up to the water surface in off-shore operations).In addition, the term uphole may refer to locations near the surface endof the borehole, less then, for example, 20 m below the earth surface.The term “downhole” may refer to locations within, or near the oppositeend of the borehole, for example, 200 m from the lower end of the drillstring or 10 m below sea level. Suitably, the drill string is providedwith a drill bit at the downhole end thereof.

It will be obvious to those familiar in the art that the same methods asdisclosed herein will work for hydraulic or pneumatically actuated (top)drives commonly found on drilling rigs.

Axial vibrations—the same impedance matching concepts can be applied tocombat axial waves travelling up and down the drill string (e.g. bitbounce).

Although explained by example as method for electric top drives, it willbe obvious to those familiar in the art that similar concepts can beused at (multiple) downhole and/or mid-string (mud)motors or turbinescommonly used in (directional) drilling. Such use could be as standalonesystem, with or without similar impedance matching systems with topdrives that may or may not be set by drillers to rotate at a (low) RPM.An example of such embodiment could be an extra system at the twist-offsensitive delicate transition between drill pipe and drill collars, orat transitions between sections of different drill pipe diameter, weightor grade.

The following paragraphs provide background information and elaborate onterms used in this disclosure. Conventions in literature are not alwaysconsistent with terms used in some of the cited publications.

Angular velocity equals rotational speed. It is expressed, for instance,in radians per second [rad/s] or in revolutions per minute (RPM) of adrill string or motor shaft.

A positive torque multiplied by a positive rotational (clockwise whenfacing downstream) speed corresponds with a positive energy flow (power)in a downstream (top drive to drill string to bit) direction.

By default, in this disclosure, torsional mechanical impedance z isexpressed in [rad/(Nm*s)]. In the electrical world the characteristicimpedance of a transmission line is normally indicated by Z, havingunits [V/A]. In the mechanical world there are two schools of modelling:

1. One treating Mechanical Speed as Volts and Mechanical Torque asAmperes; and

2. One treating Mechanical Speed as Amperes and Mechanical Torque asVolts.

In the present description, the first school of modelling is used andthus (to be consistent with the electrical naming convention) thefollowing definition of z is used:

(Torsion) characteristic impedance=z[rad/Nm*s](=(rotation)speed/torque))

Note that in the mechanical world we are also using the term “mobility”with speed/torque units ([rad/Nm*s]), which is clearer with respect tothe units. Therefore we might also label “characteristic impedance” of amechanical transmission line as the “characteristic mobility”. Herein,it is chosen to use z (with label “characteristic impedance” and units[rad/Nms]) in the control diagram where a set-point for z is calculatedfrom pipe torque and rotational speed. This in contrast to the 1/Zvalue, which has been used in other publications like SPE 18049 andwhich can be better regarded as the characteristic admittance, havingunits [Nm*s/rad].

The symbols Z and ζ may be used to indicate the characteristic impedanceof the tool string. Drive system (source) impedance may be indicated bythe symbol Z or z.

The control system of the invention comprises feedback of both torqueand rotational speed signals into a controller. An objective of saidcontroller is to maintain the drive speed over torque ratio equal to theconnected tool string impedance Z. A secondary objective, for lowerfrequencies, is to approach and maintain a setpoint speed as driverotation speed. The system includes a rotational speed sensor and atorque sensor, with the latter optionally replaced by a motor torquesignal already available from a variable frequency drive (VFD) for an ACmotor and the current safeguarding signal for a DC motor.

The present invention is not limited to the above-described embodimentsthereof, wherein many modifications are conceivable within the scope ofthe appended claims. Features of respective embodiments may for instancebe combined.

1. A method of damping vibrations in a tool string, said vibrationscomprising torsional waves propagating along said tool string, themethod comprising the steps of: instructing a drive system to rotate thetool string at a set rotational speed (Ω_(r)); determining a rotationalspeed (Ω_(r)) of the tool string; determining a torque (T) at or nearthe interface between the tool string and the drive system; determininga tool string impedance (ζ) of a section of the tool string adjacentsaid interface; calculating a rotation correction signal using thedetermined torque (T) multiplied by the determined tool string impedance(ζ); correcting the set rotational speed (Ω_(r)) using the rotationcorrection signal to provide a corrected set rotational speed(Ω_(r,cor)) signal; subtracting the measured rotational speed (ω_(r))from the corrected set rotational speed signal to provide a twicecorrected set rotational speed (Ω_(r,2cor)) signal to the drive system.2. The method of claim 1, wherein the step of correcting the setrotational speed includes: multiplying the set rotational speed by apredetermined factor; and subtracting the rotation correction signalfrom the multiplied set rotational speed (Ω_(r)) to provide a correctedset rotational speed (Ω_(r,cor)) signal.
 3. The method of claim 2,wherein the predetermined factor is
 2. 4. The method of claim 1, whereinthe step of calculating a rotation correction signal comprises:calculating a torque correction signal using the measured rotationalspeed (ω_(r)) and the inertia J of the drive system; and subtractingsaid torque correction signal from the motor supplied torque (Tm),providing a corrected torque signal (T_(cor)).
 5. The method of claim 4,wherein the step of calculating a torque correction signal includes:determining a time differential signal of the rotational speed (ω_(r))of the tool string to provide a tool string rotational accelerationsignal; amplifying the tool string rotational acceleration signal by again factor J, wherein the gain factor J is substantially equal to theinertia J of the drive system.
 6. The method of claim 5, comprising thesteps of: calculating the gain factor J using the tool string rotationalacceleration signal and the torque (T).
 7. The method of claim 6,wherein the torque signal is selected from: measured torque (Td), motortorque (Tm), and corrected torque signal (T_(cor)).
 8. The method ofclaim 1, including the steps of equally low-pass filtering the torque(T) and speed signals.
 9. The method of claim 1, comprising the stepsof: periodically adding a step pulse to the set rotational speed(Ω_(r)); determining the ratio of the amplitude of said step pulse andthe amplitude of the resulting step in observed rotational speed(ω_(r)); automatically adjusting the impedance gain value (z′)accordingly, so that said ratio approaches the value of
 1. 10. Themethod of claim 1, comprising the steps of: adding a white noise signalto the set rotational speed (Ω_(r)); calculating a tool string spatialimage via a cross-correlation function using the white noise signal andthe sum of the observed rotational speed (ω_(r)) and the rotationcorrection signal; observing from said cross correlation function theremaining discrepancy between an estimated tool string impedance and animplemented drive impedance; adjusting the impedance gain value (z′) inaccordance with the observed discrepancy; and using said adjustedimpedance gain value (z′) as updated impedance gain factor (z′) in thestep of calculating the rotation correction signal.
 11. The method ofclaim 10, wherein the cross-correlation function is periodicallycalculated at set time intervals.
 12. The method of claim 11, whereinthe cross-correlation function is calculated as background process whileidling or during steady-state operation of the tool string.
 13. Themethod of claim 11, wherein the set time interval is in the range of 10to 30 seconds.
 14. The method of claim 1, comprising the step of:providing the twice corrected set rotational speed (Ω_(r,2cor)) signalto a speed controller of the drive system, the speed controller having again of 10,000 Nms/rad or (much) more.
 15. A control system for dampingvibrations in a tool string, said vibrations comprising torsional wavespropagating along said tool string, the system comprising: a usercontrol module for instructing a drive system to rotate the tool stringat a set rotational speed (Ω_(r)); a sensor for determining a rotationalspeed (ω_(r)) of the tool string; a torque sensor for determining atorque (T) at the interface between the tool string and the drivesystem; means for determining a tool string impedance (ζ) of a sectionof the tool string adjacent said interface; a first feedback loopcomprising means for multiplying said torque (T) by the determined toolstring impedance (ζ), for providing a rotation correction signal, andfor correcting the set rotational speed (Ω_(r)) using the rotationcorrection signal to provide a corrected set rotational speed(Ω_(r,cor)) signal; a second feedback loop for subtracting the measuredrotational speed (ω_(r)) from the corrected set rotational speed(Ω_(r,cor)) to provide a twice corrected set rotational speed(Ω_(r,2cor)) signal to the drive system.
 16. The system of claim 15,comprising a third corrective mechanism to adjust the tool stringrotational speed (ω_(r)) to the set rotational speed (Ω_(r)).
 17. Thesystem of claim 15, comprising a speed controller for controlling thespeed of the drive system, the speed controller having a gain of 10,000Nms/rad or more.
 18. The system of claim 15, a downhole end of the toolstring being provided with a bottom hole assembly for drilling awellbore.
 19. The system of claim 15, a downhole end of the tool stringbeing provided with a pump device drivable by the tool string.